The existence of cyclic variability in the quality of combustion in spark-ignited, internal combustion engine has long been recognized. Such variations may be particularly severe for lean air-fuel mixtures, i.e., when the ratio of air to fuel is greater than that implied by chemical stoichiometry. The analysis of these variations is made difficult by the existence of several possible mechanisms that could act separately or in concert. One problem is the variations in the delivery of air and fuel into the cylinder. The effect of variations either in mass of fuel or its distribution tend to be exacerbated under lean conditions, when the total mass of fuel is relatively smaller. It is recognized that the fluid dynamic effects during engine intake and exhaust strokes are dominant contributors in cyclic variations. The importance of the residual gas, both content and amount, has also been recognized and is generally regarded as the cause of the frequently observed alternating pattern of high and low work output cycles, although other mechanisms have been proposed. Investigators have considered cyclic variations from the standpoint of understanding the mechanism well enough to effect a reduction in the variation by imposing control. They found that significant correlation exists between consecutive firings of a particular cylinder, and that various relevant measurable quantities, such as indicated mean effective pressure, are subject to reasonable prediction one cycle in advance. Various means of imposing control, such as through changes of spark timing and fuel delivery have been considered.
Because the combustion process depends on several state variables and is nonlinear, it is a candidate for exhibiting the complex behavior called deterministic chaos, or just chaos for short. If chaotic behavior takes place in a system with many important state variables (e.g., more than ten), it is termed high-dimensional chaos. While high dimensional chaos is in principle deterministic, it is usually so complex that as a practical matter (at least with current understanding), it can only be treated with methods applicable to stochastic (random) systems. Hence to be of present practical importance, e.g., for better fundamental understanding or real-time control of a physical system, it is necessary for the identified chaotic behavior to be low-dimensional, (e.g., have a number of important state variables that is less than ten).
Prior art has established models that generate data scatter that looks very much like that of the real data, but no one has been able to predict when the next outlier will occur. Thus, there exists a need to improve the accuracy of prediction of undesirable combustion events during lean (high air/fuel ratio) engine operation.